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As level AQA physics harmonics

A guitar string is 0.70m long. The string is tuned so that when its full length is plucked it vibrates at a frequency of 384 Hz. To play a higher note, the string is pressed so that the length free to vibrate is shorter. A fret on the neck of the guitar ensures that the correct length is produced when the string is pressed. A certain fret is positioned so that when it is used, the frequency of the note obtained is 427 Hz. What length of string is vibrating now?

I do not get this question at all

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Original post by Tayy663

Two ways of doing this question, the simplest of which is to use ratios. The product of the frequency to the length of the vibrating string is constant.

i.e.

f_1 l_1 = f_2 l_2

Alternatively it is possible to calculate the wavespeed on the string and from there calculate the wavelength corresponding to 427 Hz frequency. Then you can calculate the length of vibrating string.